The holographic entropy zoo

Abstract

We study the holographic dual of a two parameter family of quantities known as the $\alpha$-$z$ divergences. Many familiar information theoretic quantities occur within this family, including the relative entropy, fidelity, and collision relative entropy. We find explicit bulk expressions for the boundary divergences to second order in a state perturbation whenever $\alpha$ is an integer and $z\ge 0$, as well as when $z\in \{0,\infty \}$ and $\alpha \in \mathbb{R}$. Our results apply for perturbations around an arbitrary background state and in any dimension, under the assumption of the equality of bulk and boundary modular flows.

arXiv comment29 pages, 3 figures

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• Holographic Entanglement of Purification from Conformal Field Theories
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Bit threads and holographic entanglement of purification
• A principle of maximum ignorance for semiclassical gravity
• Quantum information geometry of driven CFTs
• Holographic excited states in AdS Black Holes
• Entanglement asymmetry in conformal field theory and holography
• Symmetry-resolved modular correlation functions in free fermionic theories
• A Renyi Quantum Null Energy Condition: Proof for Free Field Theories
• Scattering strings off quantum extremal surfaces
• Quantum Error Correction in SYK and Bulk Emergence
• The holographic dual of Rényi relative entropy
• Improved proof-by-contraction method and relative homologous entropy inequalities
• Proof of Renyi QNEC for free fermions
• Large and Small Corrections to the JLMS Formula from Replica Wormholes
• Information geometry encoded in bulk geometry
• Holographic Rényi relative divergence in JT gravity